A Follow-Up on Projection Theory: Theorems and Group Action

• 作者: Jean-Francois Niglio
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: PROJECTION Theory PROJECTION MANIFOLDS PROJECTORS CONGRUENT PROJECTION Matrices
• 年，卷（期）: 2019,（1）
• 页码范围: 1-19
• 页数: 19页
• 分类号: O1

摘要

In this article, we wish to expand on some of the results obtained from the first article entitled Projection Theory. We have already established that one-parameter projection operators can be constructed from the unit circle . As discussed in the previous article these operators form a Lie group known as the Projection Group. In the first section, we will show that the concepts from my first article are consistent with existing theory [1] [2]. In the second section, it will be demonstrated that not only such operators are mutually congruent but also we can define a group action on ?by using the rotation group [3] [4]. It will be proved that the group acts on elements of ?in a non-faithful but ∞-transitive way consistent with both group operations. Finally, in the last section we define the group operation ?in terms of matrix operations using the operator and the Hadamard Product;this construction is consistent with the group operation defined in the first article.